# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(t_bool,t_fun(X1,t_bool)),X2),s(t_bool,X3))),s(X1,X4)))=s(t_bool,X3)=>![X5]:![X3]:(p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),X5),s(t_fun(X1,t_bool),happ(s(t_fun(t_bool,t_fun(X1,t_bool)),X2),s(t_bool,X3))))))<=>(~(s(t_fun(X1,t_bool),X5)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))&p(s(t_bool,X3))))),file('i/f/res_quan/RES__EXISTS__NULL', ch4s_resu_u_quans_RESu_u_EXISTSu_u_NULL)).
fof(26, axiom,![X1]:![X4]:~(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(27, axiom,![X1]:![X21]:(?[X4]:p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X21))))<=>~(s(t_fun(X1,t_bool),X21)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_predu_u_sets_MEMBERu_u_NOTu_u_EMPTY)).
fof(28, axiom,![X1]:![X4]:![X22]:(p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X22))))<=>?[X23]:(p(s(t_bool,h4s_bools_in(s(X1,X23),s(t_fun(X1,t_bool),X4))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X22),s(X1,X23)))))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_bools_RESu_u_EXISTSu_u_DEF)).
fof(31, axiom,![X1]:![X5]:~(p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(t_fun(X1,t_bool),X5))))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_resu_u_quans_RESu_u_EXISTSu_u_EMPTY)).
fof(36, axiom,![X1]:![X31]:![X24]:![X19]:![X20]:(s(t_fun(X1,t_bool),X20)=s(t_fun(X1,t_bool),X19)=>(![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X19))))=>s(t_bool,happ(s(t_fun(X1,t_bool),X24),s(X1,X4)))=s(t_bool,happ(s(t_fun(X1,t_bool),X31),s(X1,X4))))=>s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),X20),s(t_fun(X1,t_bool),X24)))=s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),X19),s(t_fun(X1,t_bool),X31))))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_bools_RESu_u_EXISTSu_u_CONG)).
fof(44, axiom,![X1]:![X20]:(~(?[X4]:p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X4)))))<=>![X4]:~(p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X4)))))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_bools_NOTu_u_EXISTSu_u_THM)).
fof(49, axiom,![X27]:![X1]:![X20]:(![X4]:?[X15]:p(s(t_bool,happ(s(t_fun(X27,t_bool),happ(s(t_fun(X1,t_fun(X27,t_bool)),X20),s(X1,X4))),s(X27,X15))))<=>?[X24]:![X4]:p(s(t_bool,happ(s(t_fun(X27,t_bool),happ(s(t_fun(X1,t_fun(X27,t_bool)),X20),s(X1,X4))),s(X27,happ(s(t_fun(X1,X27),X24),s(X1,X4))))))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_bools_SKOLEMu_u_THM)).
fof(51, axiom,![X1]:![X4]:![X20]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X20)))=s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X4))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_predu_u_sets_SPECIFICATION)).
fof(53, axiom,~(p(s(t_bool,f))),file('i/f/res_quan/RES__EXISTS__NULL', aHLu_FALSITY)).
fof(54, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f)),file('i/f/res_quan/RES__EXISTS__NULL', aHLu_BOOLu_CASES)).
fof(58, axiom,![X11]:(s(t_bool,X11)=s(t_bool,f)<=>~(p(s(t_bool,X11)))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(71, axiom,p(s(t_bool,t)),file('i/f/res_quan/RES__EXISTS__NULL', aHLu_TRUTH)).
fof(74, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)<=>p(s(t_bool,X11))),file('i/f/res_quan/RES__EXISTS__NULL', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
